Compute the overall heat transfer coefficient U for a wall separating two fluids in a heat exchanger, pipe or building envelope. The tool combines the four series thermal resistances — inside film, wall conduction, outside film and fouling — and shows in real time which one is bottlenecking the exchanger.
Parameters
Inside convective coefficient h_i
W/(m²·K)
Film coefficient on the hot-fluid side of the wall
Outside convective coefficient h_o
W/(m²·K)
Film coefficient on the cold-fluid side of the wall
Clean water ≈ 0.0001, sea water ≈ 0.0003, dirty water ≈ 0.001
Results
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Inside film 1/h_i (m²·K/W)
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Wall conduction L/k (m²·K/W)
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Outside film 1/h_o (m²·K/W)
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Fouling R_f (m²·K/W)
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Total 1/U (m²·K/W)
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Overall U (W/(m²·K))
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Thermal circuit & temperature profile — animation
Heat flows from the hot fluid to the cold fluid through four series resistances — inside film, wall, fouling and outside film. The temperature drops in four steps across them.
The overall heat transfer coefficient U is the reciprocal of the sum of the four series thermal resistances. h_i, h_o: inside / outside convective coefficients [W/(m²·K)]; L: wall thickness [m]; k: wall thermal conductivity [W/(m·K)]; R_f: fouling resistance [m²·K/W]. The largest of the four resistances bottlenecks the whole exchanger.
The heat flux q [W/m²] is just the bulk temperature difference ΔT times U. Once the design duty Q is set, the required area A follows uniquely once the log-mean temperature difference ΔT_lm is known.
What is the overall heat transfer coefficient?
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"Overall heat transfer coefficient U" comes up all the time in radiators and heat exchangers. How is it different from just "thermal conductivity"?
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A common confusion. Thermal conductivity k is a property of the material itself — it only describes what is happening inside the wall. U bundles the whole journey from the bulk hot fluid through the wall and out into the bulk cold fluid into a single number: inside film, wall, fouling, outside film, all four in series, then take the reciprocal of the sum. Think of it as a convenience coefficient defined so that the heat flux is just q = U·ΔT.
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So it is series resistance. With the defaults h_i=500, h_o=100, L=50 mm, k=50 I get an outside-film resistance of 0.010 — the biggest one — and U ≈ 76 W/(m²·K). Does that mean the only thing that helps is a stronger outside fan?
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Exactly. The iron rule of series resistances is "the largest one rate-limits the whole thing". Here you have 0.002 inside, 0.001 wall, 0.010 outside, 0.0001 fouling — the outside film alone is 76% of the total. Doubling h_i from 500 to 1000 cuts the inside resistance from 0.002 to 0.001, saving 0.001. Doubling h_o from 100 to 200 cuts the outside from 0.010 to 0.005, saving 0.005. The lesson U keeps teaching is "do not waste effort on the small resistances".
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So when designing a heat exchanger you have to find the bottleneck first. Which side usually rate-limits in practice?
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Almost always the gas side. Air-cooled radiators, AC outdoor units, boiler stacks, air-cooled oil coolers — all of them. Liquid h is 500–5000, gas h is 10–200, so we add fins to the gas side to multiply the apparent area by 10–20×. That is what a finned-tube heat exchanger really is: an attack on the bottleneck. In a water-to-water exchanger both sides run h ≈ 3000, and at that point adding R_f = 0.0005 can make fouling the bottleneck instead.
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The fouling resistance worries me — that grows with time during operation, right? How do you handle it at the design stage?
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Right, over a year R_f can grow from 0 to about 0.0003. If you size to clean-U only, the unit underperforms after six months. The standard recipe (TEMA, HEI) is: take the recommended R_f from the start, work the dirty U, and then add another 20–30% on area. It is just as important to schedule cleaning so R_f never gets too big — try raising R_f in this tool and you will see the bottleneck side suddenly flip to fouling once it crosses a certain value.
Frequently Asked Questions
For a plane wall separating two fluids, the inside convective, wall conduction, outside convective and fouling resistances sit in series. U is the reciprocal of their sum: 1/U = 1/h_i + L/k + 1/h_o + R_f, with units W/(m²·K). Multiplying by the bulk temperature difference between the two fluids gives the heat flux q = U·ΔT, and the required heat-exchanger area follows from A = Q / (U · ΔT_lm).
U is the reciprocal of a sum of series resistances, so the largest single resistance bottlenecks the whole exchanger. With h_i = 500 W/(m²·K) and h_o = 100 W/(m²·K), for example, the inside resistance is 0.002 and the outside resistance is 0.010 — the outside is five times larger, so adding inside fins barely moves U. Find the longest bar in the breakdown chart and concentrate the improvement (more outside flow, higher-k wall, cleaning) on that side.
TEMA gives R_f ≈ 0.0001 m²·K/W for clean water, 0.0002–0.0004 for sea water and 0.0005–0.001 for dirty cooling water. Adding R_f = 0.0005 to a clean U = 1000 W/(m²·K) exchanger yields 1/U_dirty = 0.001 + 0.0005 = 0.0015, i.e. U_dirty ≈ 667 W/(m²·K) — a 33% loss. Standard practice is to use the dirty U for sizing and add 20–30% margin on heat-transfer area.
Wall conduction resistance is L/k. For a 2 mm stainless wall (k ≈ 16) it is L/k = 0.000125; for 2 mm copper (k ≈ 400) it drops to 5e-6 — orders of magnitude smaller. With the default k = 50 W/(m·K) (carbon steel) and a 50 mm wall, L/k = 0.001 m²·K/W, which is half of the inside film resistance 0.002 and not negligible. In a thin-plate heat exchanger (≈ 0.5 mm wall) wall resistance falls to the 1e-5 range and U is set almost entirely by the convective films.
Real-World Applications
Shell-and-tube heat exchanger design: The workhorse of refineries and chemical plants for heat recovery. With cooling water on the shell side and hot oil on the tube side, the design starts by identifying which of the four resistances is bottlenecking U, then decides on finned tubes, baffles and tube-side velocity. The fouling resistance R_f from TEMA is added from day one, the design U is taken a notch lower than the clean value, and an area margin is built in — that is the industry standard for sizing.
HVAC air-cooled coils and outdoor units: In residential air conditioners and rooftop units, the air side (h ≈ 30–80) and the refrigerant side (h ≈ 2000–5000) differ by two orders of magnitude, so air is always the bottleneck. Densely packed aluminium fins, corrugated surfaces and high-speed fans are all attacks on the bottleneck — the U formula explains in one line why every improvement is concentrated on the air side.
Building envelopes and windows: Buildings rate wall and window heat performance directly by U-value (called "thermal transmittance" in building physics). Triple glazing, insulation and air gaps are added as series resistances exactly as in this tool. Japan's energy-efficiency code sets targets such as window U ≤ 2.33 and exterior wall U ≤ 0.46 W/(m²·K) depending on climate zone, and designers size each layer with the same arithmetic this simulator uses.
Boilers and waste-heat boilers: A typical layout has radiation + convection on the flame side (h ≈ 100–300), boiling on the water/steam side (h ≈ 5000–30000) and soot fouling R_f ≈ 0.001. Sootblower scheduling on the flame side is precisely the operating practice that keeps fouling from dominating everything else — drag R_f up in the tool and you will see the bottleneck flip from the flame side to the fouling layer at a sharp threshold.
Common Misconceptions and Pitfalls
The number-one mistake is confusing U with thermal conductivity k. k is a material property with units W/(m·K); U is the whole-wall performance with units W/(m²·K) — different dimensions altogether. It is tempting to think "copper has high thermal conductivity, therefore U is high too", but when the convective side (especially a gas side) is the bottleneck, switching the wall to copper barely changes U. Sweep k from 16 (stainless) to 400 (copper) in this tool and at the default settings U hardly moves.
The next pitfall is mixing inside-area and outside-area bases. This tool treats a plane wall on a unit-area basis, but a tube has different inside and outside areas. The full equation is 1/(U_o A_o) = 1/(h_i A_i) + ln(r_o/r_i)/(2π k L_tube) + 1/(h_o A_o), and U_o (outside-area basis) and U_i (inside-area basis) are numerically different. Always declare which basis your U is on, and make sure the area A you multiply matches it; mixing them can mis-estimate the duty by 30% or more.
Finally, copying h values from a catalogue and using them as-is is dangerous. The convective coefficient h depends strongly on velocity, fluid properties and channel geometry. In-tube turbulent flow scales as h ∝ U^0.8 (Dittus–Boelter), free convection as ΔT^(1/4), boiling can differ by an order of magnitude between nucleate and film boiling. This tool treats h as an independent input, but for real design you must compute h from a Re–Pr–Nu correlation. Any error in h flows directly into U — a 20% error on the bottleneck-side h gives a 20% error on U.
How to Use
Enter the inside convection coefficient (hInsideNum) in W/(m²·K)—typical values: 5000 for water-side film, 50 for air-side film
Enter the outside convection coefficient (hOutsideNum) in W/(m²·K)
Input wall thickness (wallThicknessNum) in meters and thermal conductivity (wallConductivityNum) in W/(m·K)—steel: 50 W/(m·K), copper: 400 W/(m·K)
The simulator calculates thermal resistances in series: inside film (1/h_i), wall conduction (L/k), outside film (1/h_o), and optional fouling resistance
Overall U-value appears as W/(m²·K)—reciprocal of total thermal resistance
Worked Example
Heat exchanger with water inside tube (h_i = 8000 W/(m²·K)), steel tube wall (thickness 2 mm, k = 50 W/(m·K)), air outside (h_o = 100 W/(m²·K)). Resistances: inside film = 0.000125 m²·K/W, wall conduction = 0.00004 m²·K/W, outside film = 0.01 m²·K/W. Total = 0.010266 m²·K/W. Result: U ≈ 97.4 W/(m²·K). Adding 0.0005 m²·K/W fouling reduces U to 82 W/(m²·K).
Practical Notes
Inside resistance dominates in air-cooled exchangers (h_o ≈ 50–150); outside resistance dominates in water-cooled designs (h_i ≈ 5000–10000)
Wall conduction negligible for thin metallic barriers; becomes significant with brick or concrete (k ≈ 0.5–1.5 W/(m·K))